It should work with those settings why do you expect it to say it failed to meet the required settings

The fact that it fails to install is a problem that will need to be fixed

Well ..., I was under the impression, it needs not to install under these poor settings.
Let's rephrase my expectation 'Installation must succeed if the pre-installation check passes'. A solution may address either side.

Without knowing why "installation freezes" there is little to do here. Is it really freezing because of the memory? There are no uploads in the install app so upload size is no issue here. POST size should also not be an issue. Time may be a problem on a lower end configuration. But this is all blindly guessing without any real data on the underlying issue.

Can you please which version of joomla you were trying to install?

@brianteeman Build: 3.8.12 is given in Issue Tracker.

I tried to install 3.8.12. (I noted this in a form field when creating this issue, but have no idee, where this is shown now).
Freeze means: The page with the progress bar appears. The progress bar advances somewhere near 20%, The Joomla logo is spinning. This for at least 30 minutes. Of course, I can close the browser (firefox), but nothing more meaningfull.

This happens on Windows 10 with XAMPP. The interessting thing: changing the settings to the recomended values and the installtion succeeds in less than a minute.

If it "freezes" that generally means a non-JSON response was returned from the server (you can see this on the network tab of your browser's developer console), and that breaks the JavaScript for the installation app. And when that happens that generally means there was some kind of fatal error. In your case, it could very well be PHP running out of memory.

changing the settings to the recomended values and the installtion succeeds

What recommended values?

Recomended values: https://docs.joomla.org/J3.x:Installing_Joomla/en
memory_limit - Minimum: 64M Recommended: 128M or better
upload_max_filesize - Minimum: 20M
post_max_size - Minimum: 20M
max_execution_time: At Least 120 Recommended: 300

Here's the key phrase, just above that:

The values for PHP.ini below are suggested values only.

The POST and upload sizes are decent to allow large file uploads (large images, our core ZIP packages are sitting at around 13 MB). These values being decent though only impacts Joomla use when it comes to upload actions (core/extension updates, image uploads, etc.).

Max execution time is an arbitrary change, if something is failing at 30 seconds you've got bigger problems in all honesty.

As for memory limit, this one really needs to be benchmarked if we're going to do anything with it. IIRC core PHP starts this value at 128M or 256M, there really should be no need to ever lower it and if someone is doing that then I'd say that's an issue they need to sort out (or the hosting provider doing it needs to be talked to).

I benchmarked the installtion process with this configuration:

 Install File: Joomla_3.8.12-Stable-Full_Package
 Install Sample Data: Default English (GB) Sample Data	
 Database Type 	mysqli
 Host Name 	localhost
 Username 	joomla
 Database Name 	joomla
 Table Prefix 	jo_
 Old Database Process 	Remove 

It appears max_execution_time is the relevant setting. A value below 40 causes the symptoms described.
I think a pre-installation check against a value below 50 shoud be added. This will prevent user frustation and it will guide the user to proper php settings.

Set to "closed" on behalf of @jwaisner by The JTracker Application at issues.joomla.org/joomla-cms/22057

Closing as it has been noted this is not a bug with Joomla and that the host settings may need checked/adjusted.